For Maxwell's equations to be valid, it is assumed that the field
vectors are \emph{single-valued}, \emph{bounded},
\emph{continuous} functions of position and time and have
\emph{continuous derivatives}. Electromagnetic fields have these
characteristics except for when there are abrupt changes in charge
and current densities. This usually occurs at interfaces between
media. The variations of field across such interfaces are related
to the discontinuous charge and current distributions by what are
referred to as \emph{boundary conditions}. Thus a complete
description of the field vectors at any point (including
discontinuities) at any time requires not only Maxwell's equations
in differential form but also the associated boundary conditions
\cite{Balanis:1989}.
